🧮 algebra

1. Let's start by stating the problem: We want to understand how to solve percent equations, which are equations involving percentages. 2. The general formula for percent problems

1. Énonçons le problème : résoudre le système d'équations différentielles vectorielles $$\mathbf{y}' = A\mathbf{y} + \mathbf{b}$$ où $$A = \begin{pmatrix}1 & 0 & 0 \\ 0 & 1 & 1 \\

1. The test covers solving linear equations, writing equations from word problems, percentages, proportions, and using the distributive property. 2. For solving linear equations li

1. **Stel het probleem vast:** We willen het volume van een betonnen bloembak berekenen die gevuld wordt met potgrond. 2. **Gegeven afmetingen:**

1. The problem asks to find $fg(1)$, which means we need to find the value of the function $f$ evaluated at $g(1)$. 2. To solve this, we first need to know the definitions or expre

1. **State the problem:** Solve the equation $7x - 5(x - 7) = 8x - 13$ for $x$. 2. **Apply the distributive property:** Expand $-5(x - 7)$ to get $-5x + 35$.

1. The question asks why the function was not evaluated at $f(1)$. 2. To evaluate $f(1)$, you substitute $x=1$ into the function's formula.

1. **State the problem:** We are given the function $f(x) = 3x + 1$ defined on the domain $0 \leq x \leq 2$. We need to find the range of this function. 2. **Recall the formula and

1. The problem is to solve a math question suitable for 4eme (8th grade) level in informatique (computer science), but since no specific problem is given, let's consider a common a

1. **State the problem:** Solve the system of equations using elimination: $$-5x + 9y = -37$$

1. The original problem involves simplifying an expression with a bracketed term from step 3, say $\left(\frac{a}{b} + c\right)$.\n2. As requested, we rewrite the bracketed term as

1. We start with the expression inside the brackets from step 3, which we denote as $\left(\frac{a}{b} + c\right)$. 2. According to your request, we rewrite this expression as a fr

1. **State the problem:** Simplify the expression $$\left( \frac{3x^{\frac{3}{2}}y^3}{x^2 y^{-\frac{1}{2}}} \right)^{-2}$$. 2. **Apply the quotient rule for exponents:** When divid

1. **State the problem:** Judy and Faith each bought equal sizes of material to make tablecloths. Judy used $\frac{7}{12}$ of her material, and Faith used $\frac{5}{8}$ of her mate

1. **State the problem:** Simplify the expression $$\frac{16y x^4}{6x^8 y^2}$$. 2. **Write the formula and rules:** When simplifying fractions with variables, divide coefficients a

1. **State the problem:** Solve the equation $$\frac{x}{2} + x + \frac{97}{12} = 0$$ for $x$. 2. **Combine like terms:** To combine the terms with $x$, express all terms with a com

1. **State the problem:** Simplify the expression $$\frac{10p^4}{6p^2}$$. 2. **Recall the rules:** When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n

1. Problem: Simplify the expression for the cost of a dress after a 6% tax, given by $d + 0.06d$. 2. Formula: When adding like terms, add their coefficients.

1. **State the problem:** Simplify the expression $\sqrt{200} - \sqrt{32}$. 2. **Recall the rule:** The square root of a product can be written as the product of square roots: $\sq

1. **State the problem:** We want to find the percent decrease of a fraction when its numerator is increased by 20% and its denominator is increased by 50%. 2. **Set up the origina

1. **State the problem:** Solve the system of equations using the elimination method: $$3x - 2y = 38$$